Resolver (2)^{-1}+[2/3-2^-1*((2/3)^-2*2/3+5^0)]^-1=

$$( 2 ) ^ { - 1 } + [ \frac { 2 } { 3 } - 2 ^ { - 1 } \cdot ( ( \frac { 2 } { 3 } ) ^ { - 2 } \cdot \frac { 2 } { 3 } + 5 ^ { 0 } ) ] ^ { - 1 } =$$

Avaliar

$$-\frac{17}{14}\approx -1,214285714$$

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some -2 e 1 para obter -1.

$$2^{-1}+\left(\frac{2}{3}-2^{-1}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

Calcule 2 elevado a -1 e obtenha \frac{1}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-2^{-1}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

Calcule 2 elevado a -1 e obtenha \frac{1}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

Calcule \frac{2}{3} elevado a -1 e obtenha \frac{3}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\frac{3}{2}+5^{0}\right)\right)^{-1}$$

Calcule 5 elevado a 0 e obtenha 1.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\frac{3}{2}+1\right)\right)^{-1}$$

Some \frac{3}{2} e 1 para obter \frac{5}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\times \frac{5}{2}\right)^{-1}$$

Multiplique \frac{1}{2} e \frac{5}{2} para obter \frac{5}{4}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{5}{4}\right)^{-1}$$

Subtraia \frac{5}{4} de \frac{2}{3} para obter -\frac{7}{12}.

$$\frac{1}{2}+\left(-\frac{7}{12}\right)^{-1}$$

Calcule -\frac{7}{12} elevado a -1 e obtenha -\frac{12}{7}.

$$\frac{1}{2}-\frac{12}{7}$$

Subtraia \frac{12}{7} de \frac{1}{2} para obter -\frac{17}{14}.

$$-\frac{17}{14}$$

Fatorizar

$$-\frac{17}{14} = -1\frac{3}{14} = -1,2142857142857142$$